Note on an apparently forgotten theorem about solid rigid dynamics

We re-derive a general procedure to substitute any rigid body by an equivalent system of exactly four masses, located at the vertices of an irregular tetrahedron

Path tracking and stability of a rolling controlled wheel on a horizontal plane by using the nonholonomic constraints

This paper studies the stabilization, tracking of a predefined trajectory and how to reach a desired set point for a wheel which is rolling on a horizontal plane without slipping. For this purpose, the wheel is controlled by small torque generated by internal servomechanisms whose dynamics can be neglected. An efficient procedure to determine the kinetic energy of the wheel is developed by introducing a set of reference systems, which in combination with the Lagrange equations with multipliers allow deriving the mathematical model of the rolling wheel. In this model, the Euler angles, the coordinates of the plane–wheel contact point and a control law of proportional+integral+derivative (PID) type provide an efficient computational procedure to track arbitrary trajectories. It is shown that the nonholonomic constraints are fulfilled with admissible reaction forces, even when the desired trajectory has cusp points. A circumference and a family of astroids are used as trajectories to verify the motion conditions derived from the energy conservation and dynamical equilibrium of the wheel along such trajectories. The results of the analytical calculations are corroborated through numerical simulations

Carbene-Controlled Regioselective Functionalization of Linear Alkanes under Silver Catalysis

Control of the regioselectivity in the functionalization of C–H bonds of linear alkanes C2H2n+2 via carbene transfer from diazo compounds is restricted to the use of rhodium-based catalysts, which govern the reaction outcome employing donor–acceptor diazo reagents. At variance with that catalyst-controlled strategy, we present an alternative approach in which employing the appropriate silver complexes containing trispyrazolylborate ligands as catalysts with large differences in their steric and electronic properties, the regioselection is mainly governed by the diazo reagent, which leads to the functionalization of primary or secondary sites of linear alkanes (lacking any activating or directing groups). Donor–acceptor aryl diazoacetates exclusively provide the functionalization of the secondary sites of hexane or pentane, whereas acceptor ethyl diazoacetate leads to an unprecedented level of primary functionalization.We thank to Ministerio de Ciencia e Innovación for Grant PID2020-113797RB-C21. We also thank Junta de Andalucía (P18-1536) and Universidad de Huelva (P.O.Feder UHU- 202024). M.A. thanks Junta de Andalucia for a postdoctoral fellowship

Podomorfos y grafitis rupestres de la ermita de San Pascual (paraje del Canastell, Crevillent, Alicante)

Se presenta un conjunto de insculturas y grafitis sobre soporte rupestre entre los que destacan una serie de motivos podomorfos, localizados en el paraje rural del Canastell, en Crevilllent, Alicante. En las últimas décadas este tipo de manifestaciones han generado un interés creciente entre los investigadores, a pesar de lo cual aún resultan escasos los conjuntos bien conocidos y documentados en la región mediterránea

Estimation of the virial coefficients by means of chaotic oscillations of pressure and density: Application to quantum gases with cubic equations of state

This paper analyzes how to determine the virial coefficients B and C of real gases by using a theoretical device whose pressures and densities oscillate in chaotic regime. The device is formed by a valve, a pressure controller, a pressure probe and a gas accumulator, for which the thermodynamic model has been derived from the force-mass-energy balances. This model allows keeping the gas temperature almost constant with chaotic oscillations in the inlet to the accumulator. The chaotic data are used to obtain variability in the pressures and densities, so that they can be used as experimental values from which the virial coefficients are estimated. For this purpose, several cubic and high precision equations of state for polar and non-polar gases and mixtures are used. In particular, the virial coefficient B for dry air is estimated by using high precision state equations, whereas, the virial coefficients B and C are also estimated for quantum gases (He4, He3 H2, D2, Ne) by using several modified cubic equations of state at moderate and high pressures. Furthermore, the values for the virial coefficient B obtained from numerical simulations are used to estimate the intermolecular potential and the radial distribution function. The results are in good agreement with the currently known experimental data for virial coefficients published in the literature

Diseño conceptual de una estación experimental de tratamiento de aguas residuales domésticas orientada a Municipios con población menor a 30.000 habitantes.

Se presenta el diseño conceptual de una planta experimental de tratamiento de aguas residuales para poblaciones menores de 30.000 habitantes. El diseño integra seis esquemas de tratamiento interconectados, incluyendo sistemas convencionales y no convencionales, con disposición final del efluente a un cuerpo de agua o infiltración lenta en el terreno, cumpliendo con la norma vigente en Colombia. El proceso incluyó una revisión del estado del arte, el diseño de plantas de este tipo como la planta de Carrión de los Céspedes (Andalucía-España), la planta UFMG/COPASA (Minas Gerais-Brasil), los trabajos realizados en Colombia del IDEAM-CINARAUTP y los ensayos realizados por Madera, Silva y Peña del CINARA en planta piloto. El área estimada para la construcción de los esquemas propuestos es de 18.000 m2 y los costos fijos de construcción de la planta se estiman en 850 millones de pesospara tratar un caudal de 1,5 l/s de agua residual doméstica

Tourist Clusters in a Developing Country in South America: The Case of Manabì Province, Ecuador

Societies nowadays shape their history by establishing traditions, customs, artisan expressions and, in short, the cultural heritage that represents them as a people in symbiosis with their natural environment. The present investigation analyzes the tourist phenomenon that has developed around intangible cultural heritage and natural heritage in the province of Manabí (Ecuador). Three types of visitors were identified in terms of motivation schemes; these three types were considered valid and useful for segmenting within the province of Manabí as a tourist destination. The conclusions suggest the need to conceive tourism products that improve the image of the destination and, at the same time, enable the sustainable management of the destination itself

Stability and chaotic behavior of a PID controlled inverted pendulum subjected to harmonic base excitations by using the normal form theory

In this paper we investigate the stability and the onset of chaotic oscillations around the pointing-up position for a simple inverted pendulum that is driven by a control torque and is harmonically excited in the vertical and horizontal directions. The driven control torque is defined as a proportional plus integral plus derivative (PID) control of the deviation angle with respect to the pointing-down equilibrium position. The parameters of the PID controller are tuned by using the Routh criterion to obtain a stable weak focus around the pointing-up position, whose stability is investigated by using the normal form theory. The normal form theory is also used to deduce a simplified mathematical model that can be resolved analytically and compared with the numerical simulation of the complete mathematical model. From the harmonic prescribed motions for the pendulum base, necessary conditions for chaotic motion are deduced by means of the Melnikov function. When the pendulum is close to the unstable pointing-up position, the PID parameters are changed and the chaotic motion is destroyed, which is achieved by employing very small control signals even in the presence of random noise. The results of the analytical calculations are verified by full numerical simulations

Smithing work in Islamic Ceuta

Se estudian en este trabajo los artefactos metalúrgicos exhumados en una excavación arqueológica preventiva llevada a cabo en el casco urbano de Ceuta, en conexión con una estructura de combustión que se ha interpretado como un hogar de forja. En paralelo a lo que sucede en otros asentamientos islámicos medievales de las costas de la Península Ibérica, se relaciona este tratamiento de minerales de hierro con la construcción naval. Se incide en la importancia de esta actividad desde al menos el siglo VI d.C. y su etapa de apogeo a partir de la segunda mitad del siglo XII con el establecimiento de la escuadra almohade en esta ciudadIn this article are studied the archeometallurgical remains exhumed in an archaeological excavation located in the centre of Ceuta (Spain, North Africa), in connection with a structure of combustion that has been interpreted like a forging workshop. As happens with other medieval Islamic settlements on the coasts of the Iberian Peninsula, the treatment of iron ores is related to shipbuilding industry. The importance of this activity is palpable since the 6th century, but even more in the second half of the twelfth century with the establishment of the almohade fleet in the cit

Evaluación de sistemas de tratamiento en lixiviados provenientes de un relleno sanitario maduro: caso relleno sanitario Curva de Rodas

RESUMEN: Los lixiviados producidos en el relleno sanitario clausurado Curva de Rodas de la ciudad de Medellín se catalogan como “lixiviados maduros”, estos se caracterizan por ser un residuo poco biodegradable. En este trabajo se evalúa la eficiencia de cinco posibles tratamientos fisicoquímicos: adsorción con 5 tipos de carbón activado granular (CAG), adsorción con Zeolita tipo A, oxidación Fenton, precipitación química con Ca(OH)2 y coagulaciónfloculación con Sulfato de Aluminio Tipo A. Mediante la adsorción con CAG se alcanzaron remociones de hasta 39% para DQO y 50% para Color. En el caso de adsorción con Zeolita tipo A se lograron remociones de hasta 3% en DQO y 7% en Color. En los ensayos de precipitación química se lograron remociones máximas de 16% en DQO y 50% en color y por el proceso de coagulación-floculación hasta del 27% en DQO y del 63% en color. Los mejores resultados se obtuvieron con el proceso de oxidación Fenton, neutralizando con NaOH se lograron remociones máximas de 95% en DQO y 97% en color. Al neutralizar con lixiviado sin tratar las remociones alcanzadas fueron de hasta 79% en DQO y 87% en color.ABSTRACT: Leachates produced in the closed landfill Curva de Rodas in Medellin, Colombia are catalogued as mature leachates. These are characterized as poorly biodegradable waste containing organic compounds such as fulvic and humic acids, heavy metals, ammonia, nitrogen, and salts. In this paper five possible physicochemical leachate treatments are evaluated: adsorption with five types of granular activated carbon (GAC), adsorption with zeolite type A, Fenton oxidation, chemical precipitation by Ca(OH)2, and coagulationflocculation with aluminum sulfide type A. The treatments are compared in terms of their capacity to remove Chemical Oxygen Demand (COD) and color. GAC adsorption removals of up to 39% for COD and 50% for color were achieved. In the case of the adsorption with zeolite type A, negligible removals of COD and color were achieved (3% and 7% respectively). Removals using the Fenton oxidation and neutralization with NaOH reached up to 95% for COD and 97% for color. When additionally neutralized with raw leachate the removals were up to 79% for COD and 87% for color. Finally in the chemical precipitation tests, removals of 27% for COD and 63% for color were achieved. Clearly, Fenton oxidation was identified as the most appropriate treatment process